If you reach a wide crevasse when you’re climbing a mountain, you have but one choice: Turn around. If you can find another path, you still may reach your destination. Otherwise, it’s time to pack it up.

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US Treasury Secretary Jack Lew has warned that pushing talks over the debt ceiling to the last minute could be "very dangerous".

So it is with negotiations that grind to a halt, according to Washington, DC-based attorney Andrew J Sherman, part of the global mergers & acquisitions practice of law firm Jones Day.

Few faltering negotiations in business have as much at stake as the budget impasse in the US Congress that has kept 800,000 federal workers home, shuttered national parks and disrupted vital public services. But in politics and commerce, there are ways to find a path forward for everyone, even after it seems that all hope is lost.

Find another route

For starters, if a negotiation has hit an impasse, consider the mountain analogy and backtrack to find another way around the obstacle. Remember what brought you to the table in the first place and consider the other party’s point of view, said Sherman, whose firm has 2,400 lawyers around the globe. Then make an attractive offer.

If you were trying to rent space in a Shanghai office building, you might say: “I want a location in one of Asia’s fastest growing cities. You want a good tenant.”

What, exactly, could US politicians backtrack to? Simple, said Sherman: remember they “came to serve and govern.”

Watch for signs you’ve lost momentum

It is much easier to rescue a negotiation that has just started to go off track than to save one that has completely derailed. The key is to remain alert to the merest hint of something going wrong.

For instance, if the other party has gone quiet, don’t let the conversation languish. Instead, ask the other party the reason for the silence, Sherman said.

Issue a mea culpa

Apologies are not pleasant, but are sometimes required.

“Probably the biggest source of sourness is the … the loss of trust. You just can’t get past that, no matter what, unless you solve that,” said Nat Wasserstein, managing director of New York-based Lindenwood Associates, a crisis management consulting firm. He recommends addressing the problem head on. Ask the other party what it thinks has caused mistrust. “It has to be dealt with,” he said.

Wasserstein remembered a contract negotiation in which his client exaggerated to a large company that he could bring more to the table than he could. Eventually, the client admitted that he had gotten a bit carried away. Had he not come clean, the deal would have fallen through, and the client’s company likely would have failed. “I had to get him to air the dirty laundry,” said Wasserstein. The mea culpa worked, and the deal was completed.

It sounds obvious, but it bears repeating. When you apologise, stick to the truth.

Bring in a third party

The Harvard Program on Negotiation at the Harvard Law School identified three situations where using a third party to negotiate was important. The first two might seem obvious: geography or a lack of knowledge typically call for hiring an outside negotiator. The third: when a relationship has foundered or wasn’t great to start with.

“By bringing in an agent, you can calm tempers and better ensure that talks are businesslike and amicable,” the Project reported. The best choice is typically an unaffiliated party — someone who has enough objectivity to be trusted by both sides —Sherman said. College professors and mediation specialists are two possibilities. You may simple need someone friendly who can bring people together over coffee or a pint of beer and say, ‘Hey, what’s going on here?’

Presidents and vice presidents have sometimes played that role in Washington. Former US president Bill Clinton, for example, famously tacked to the center between liberals in his own party and conservatives and moderates on both sides of the aisle. US Vice President and longtime former Senator Joe Biden in 2011 successfully negotiated budget and debt ceiling pacts.

Adjust your expectations

Coming to a deal might mean letting go of your illusions, said Marjorie Conner, counsel at Dentons US, who has negotiated many telecommunications deals. This is particularly important when you are negotiating with a party that has more power than you.

Understand what lies beneath

It helps to know what might be motivating someone to ask for something that seems unreasonable. Barry Goldman, professor at the Eller College of Management at the University of Arizona, remembered when a fellow lawyer’s pay deal got hung up on an additional $50,000 compensation demanded by the lawyer. The partner leading the new firm's negotiation asked a simple question: "Why?"

It turned out the attorney had a disabled son whose care costs led to tremendous out-of-pocket expenses. The new firm added a $10,000 rider to its health plan, and the deal was saved. "They got beyond the projection, to the interest beneath," Goldman said.

Take your co-party out to lunch

Conner recalled a deal that had stalled for no obvious reason. She phoned the lawyer for the other side and invited him to lunch. They talked about everything but the negotiations.

“Talk about kids, talk about whatever,” she said. “I watched him swill white wine for the three hours.” That deal didn’t come through, but the lawyer later brought other business to her client.

That is perhaps the final lesson of negotiations that have gone sour: not all deals are meant to happen. Sometimes a negotiation is just a long, expensive decision-making process that yields the conclusion that the deal was never a good idea in the first place. “Your job is not to put Humpty Dumpty back together again,” said Sherman.

In business, a broken deal usually is not a true catastrophe. But in the case of the US budget, the failure of politicians to negotiate their icy communication crevasse could have ruinous consequences.